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Given a set of correlated securities and their corresponding closing prices, I am looking for a way to construct an index of these securities.

When applying PCA to obtain the principal components, how can I use or understand the output to construct an index?

For instance in matlab:

[coeff,score,latent,tsquared,explained,mu] = pca(prices)
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  • $\begingroup$ Not sure I understood what you are trying to do. The eigenvector i from the PCA is in fact the weights of an index that would track the -ith principal component. $\endgroup$
    – Alex C
    Commented Apr 24, 2017 at 0:21
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    $\begingroup$ Hmm clear. But if you choose lets say the first two PC to explain the variation, how do you derive then the weight for the j-th asset? $\endgroup$
    – WJA
    Commented Apr 24, 2017 at 0:24
  • $\begingroup$ I don't know. I would form a linear combination of the first two PC, weighted by the square roots of the respective eigenvalues (so the volatilities are properly taken into account). $\endgroup$
    – Alex C
    Commented Apr 24, 2017 at 0:40

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